Rewrite as a simplified fraction. ${0.1\overline{16} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 116.1616...\\ 10x &= 1.1616...\end{align*}}$ Subtracting the two equations, we have: ${990x = 115}$ ${x = \dfrac{115}{990}} $ ${x = \dfrac{23}{198}} $